Hi Ania,
The FIRST robotic competition looks very interesting, especially because high school students can involve in it too. Do you or your older kid have experience with this league? My younger daughter Yanran is more math/engineering oriented although she denies that. It is not cool to be an engineer. But I may be able to convince her to give robotics another try.
Yanran was in robotics team when she was in middle school. As one of few girls in the team, she did not have that great a time. I think that Yanran did not quite get the idea of programming at that time. She is much better equipped now.
The robotics kit that they were using is Lego Mindstorms
http://shop.lego.com/Product/?p=8527 This is NO toy. It has motors, gears, sensors, blocks, etc. Putting things together is easy. The hard part is to program the robot to do the things that you want them to do, like getting out of a maze by touching the walls.
The Mindstorms kit is about $250 each. Well worth it for what it can do but you will need parent volunteers who have programming or engineering background to get anything going.